The present invention relates generally to methods and apparatuses for improving the accuracy of, and reducing errors in, the position measurements of stand alone navigation and differential navigation receiver system. The present invention is oriented to the improvement of characteristics of a navigational receiver working with navigational Satellite Positioning System signals (SATPS, in particular GPS and/or GLONASS), and using the code measurements and the integrated carrier phase measurements.
For the positioning of a navigational roving receiver, one uses radio signals received from a plurality of Satellite Positioning System (SATPS) satellites, and in particular GPS and/or GLONASS satellites. The receiver""s position is known if its coordinates in a particular coordinate system (for example, Earth-Centered-Earth-Fixed coordinate system) are known.
The time scale of any receiver (including a roving receiver) usually has some casual offset with respect to the SATPS system time. The value of this time offset is determined simultaneously with the determination of the position coordinates. In this case, for the determination of three coordinates of a roving receiver, it is usually necessary to receive navigation signals from not less than four navigational satellites. However if one of the receiver coordinates is considered to be known (e.g., a two-dimensional solution is used and the height is known or assumed), it is usually necessary to receive navigational signals from not less than three navigational satellites.
FIG. 1 shows a simplified form of the Satellite Positioning System (SATPS) operation in the Stand Alone Navigation (SAN) mode. (Stand Alone Navigation corresponds to an absolute positioning system, i.e. a system that determines a receiver""s position coordinates without reference to a nearby reference receiver). The roving receiver 1 and its corresponding antenna 3 are located on the ground surface, or in the near Earth space, and can receive signals from navigational satellites 7, 9, 11, and 13. The receiver position is defined by its coordinates in a particular coordinate system, for example the Earth-Centered-Earth-Fixed (ECEF) system. It is supposed that the exact position of the receiver is unknown, and that the receiver has the task of generating an estimate of the receiver""s position within a given accuracy. That accuracy depends upon the number of available satellites, the configuration of the satellites, the quality of the receiver, and a number of other factors.
FIG. 2 shows a simplified form of the SATPS operation in the Differential Navigation (DGPS) mode. In the differential mode, the reference receiver 15 evaluates/estimates the slowly varying components of-measurement errors and generates scalar or vector corrections for each visible navigational satellite. These corrections are sent to the roving SATPS receivers which are configured to use the corrections and which are near enough to the reference receiver for the corrections to be useful. (This explained in greater detail at page 4 of Parkinson, et al, Global Positioning System: Theory and Applications, Volume II, American Institute of Aeronautics and Astronautics, Inc., 1996, herein referred to as xe2x80x9cParkinson Vol. IIxe2x80x9d)
In one implementation, the roving receiver 1 receives, by means of the modem 5, differential correction signals generated and sent by the reference receiver 15, by means of the modem 19. By means of the antenna 3, the roving receiver 1 receives signals from navigational satellites 7, 9, 11, and 13, and processes them together with the differential corrections. In other implementations, other communications means besides modems 5 and 19 may be used, and more than four satellite signals may be used.
The navigational signals broadcast by navigational satellites 7, 9, 11, and 13, are received by the antenna 3 of the roving receiver 1 and by the antenna 17 of reference receiver 15. (The number of navigational satellites in the general case must be four or more, but if one of the coordinates of the roving receiver is known, the number of navigational satellites must not be less than three.) Both of receivers 1 and 15:
separate the received signals and identify the navigational satellites (define the satellite number or its corresponding index) for each received signal;
a determine the current position (coordinates) of each of the observed navigational satellites 7, 9, 11, and 13, using the transmission delay of the satellite""s code signal and the information on satellite""s Ephemeris, which is conveyed by a low frequency (50 Hz) signal which is modulated onto the satellite""s code signal; and
track the code signal delay over time and determine the integrated carrier phase for each navigational signal (the satellite""s code signal is modulated onto a higher frequency carrier signal).
The antennas 3, 17 and the receivers 1, 15 of navigational signals are the user portion of the SATPS (in particular GPS and/or GLONASS).
Snapshot Position Solutions
A xe2x80x9csnapshot position solutionxe2x80x9d, or simply xe2x80x9csnapshot solutionxe2x80x9d, is a determination of the receiver""s position coordinates at a particular instant of time using the pseudorange code measurements from the satellites at that particular instant of time. The snapshot position solution does not use information from previous time points (e.g., previous epochs). In addition to the code delay information, a snapshot position solution may also use carrier phase information. A snapshot solution of the receiver coordinates is usually formed by application of the least squares method (LSM) to the pseudorange code measurements, obtained for one epoch (for a certain moment of time). The LSM method is explained in greater detail at pages 412-413 of Parkinson, et al., Global Positioning System: Theory and Applications, Volume I, American Institute of Aeronautics and Astronautics, Inc., 1996, herein referred to as xe2x80x9cParkinson Vol. Ixe2x80x9d, as well as by other references.
The magnitude of error in the snapshot solution is related to the errors in the pseudorange code measurements, the number of satellites used in the snapshot solution, and the geometry of navigational satellites. The snapshot error is reduced by reducing the errors in the code measurements, by increasing the number of satellites in the solution, and by having the satellite""s configuration near to the optimal constellation configuration (which is well known to the GPS art). Errors in the pseudorange code measurements are caused by the presence of thermal and other noises at the receiver""s input, as well as by a number of reasons, amongst which the following ones are the most significant (see Parkinson Vol. I, page 478):
Errors in the transmitted Ephemeris data;
Errors in the satellite (transmitted) clock, including those caused by Selective Availability;
Ionospheric refraction;
Tropospheric refraction;
Multipath reflections.
The error in the receiver coordinate estimates caused by the number of satellites and by their specific geometry is characterized by the value of a geometric factor called the geometric dilution of precision (GDOP) (see Parkinson Vol. I, pages 413, 420, 474.). When the number of observed navigational satellites is reduced, which is often caused, for example, by the short-term shadowing or blocking of one or more of the satellites, the value of the dilution of precision can sharply increase, which in turn results in a substantial increase in the errors of the coordinate estimates.
As is typically done in the global positioning art, the errors in the receiver""s position and time scale caused by the above-identified error sources are estimated by statistical methods using a simulation model of the receiver and the satellites. Each error source, such as thermal noise in the receiver or clocking errors in the satellite signals caused by Selective Availability, is modeled as a random noise source having a representative probability distribution. Oftentimes, a Gaussian distribution is used. The width of the distribution may be determined empirically and is usually represented by a root mean square (RMS) value, which is also called a standard deviation value. By convention, these RMS values are oftentimes stated in units of meters. The simulation model is able to place the receiver and satellites in known positions at a selected time moment, and is then able to randomly select values for the error sources which are within the respective probability distributions for the sources. If there is some degree of correlation between any two random variables, the simulation model can be made to account for the correlation. The simulation model can then compute the position of the receiver under the influence of that particular set of randomly-selected values for the error sources. The difference between the computed position and the known position previously set by the simulation model shows the amount of error in the receiver""s coordinates and time scale caused by that set of randomly-selected values for the error sources. The computation process can be repeated several hundred times using new random values each time, but with the receiver and satellites held in fixed positions, to create a set of samples of the receiver""s computed position and time scale. An error probability distribution for each of the receiver""s position coordinates can then be computed from this set of samples. An error distribution for the receiver""s time scale can also be computed. Each probability distribution can be characterized by a mean value, which is the average value for the samples in the distribution. Using the receiver""s X-position coordinate as an example, the estimation of mean error for this coordinate is computed as follows:             Measured mean error of  X-coordinate        =                  [                              (                          1              /              M                        )                    ·                                    ∑                              k                =                1                            M                        ⁢                          x              k                                      ]            -              x        true              ,
where M is the number of samples, where k is an integer which indexes the samples in the set, where Xk is the k-th computed sample for the X-coordinate, and where xtrue is the X-coordinate of the receiver""s position, as set by the simulation model. While this computed value of mean error is based on a simulation model, it is a good estimate of the mean error that would be present in a real measurement, provided that the noise sources have been properly characterized and modeled. For this reason, we will refer this computed value as a xe2x80x9cmeasured mean errorxe2x80x9d.
Each probability distribution can also be characterized by a standard deviation from the measured mean value, or what we refer to as the xe2x80x9cmeasuredxe2x80x9d root-mean-square (RMS) error. The measured RMS error (estimation of standard deviation) is representative of the width of the probability distribution on either side of the measured mean value. Using the receiver""s X-coordinate as an example, the measured RMS error for this coordinate is computed as follows:       Measured RMS error of  X-coordinate    =            {                        1          /                      (                          M              -              1                        )                          ·                              ∑                          k              =              1                        M                    ⁢                                    [                                                x                  k                                -                                                      1                    /                                          (                      M                      )                                                        ·                                                            ∑                                              j                        =                        1                                            M                                        ⁢                                          x                      j                                                                                  ]                        2                              }              1      /      2      
We typically use between 300 and 3,000 samples to compute the measured means and RMS errors. The measured RMS error and measured mean error are preferably computed from the same set of samples.
Our discussion of the prior art and the present invention will look at the effects of dynamic movements of the receiver upon the measured position and time scale. The effects of dynamic movements can best be seen in the measured mean error. In linear receiver systems in which all of the noise sources have zero mean values (but non-zero RMS values), measured mean errors that occur in the receiver""s position and time scale are solely due to the dynamic movements in the receiver. In this case, we may call the measured mean error the dynamic error. (In general, this cannot be said for non-linear systems, or for linear systems where there are error sources which have non-zero mean values.)
A simulation of SATPS and roving receiver was performed to estimate the impact of discontinuities in the geometric dilution of precision on the accuracy of SATPS snapshot estimates. The results of simulation are presented on FIGS. 3-8.
FIGS. 3-5 show the measured root-mean-square error (RMS) of the snapshot estimate of the X, Y and Z coordinates versus time when some of the observed navigational satellites are shadowed so that number of observed satellites is reduced from a large number (e.g., 11) down to four. The calculated value of dilution of precision is in correspondence with the definition given by Parkinson, Vol. I, page 474 for the corresponding coordinate (x, y, and z), and increases in this scenario in spurts (stepwise) on the value indicated in FIGS. 3-5.
The scenario used to generate the results presented in FIGS. 3-5 is as follows. During the time interval 0-99 s, the number of observed navigational satellites (GPS) is at a relatively large value of 11. At the moment of time t100=100 s, the number of observed navigational satellites is reduced to four, which leads to an increase (discontinuous change) in the dilution of precision. At the moment of time t300=300 s, the number of observed navigational satellites increases back to a relatively large number of ten. In the simulation, the noise in each pseudorange code measurement is assumed at a RMS value of 3 m. The Selective Availability is represented by an analytic model (see Parkinson, Vol. 1, pages 614-615) with an RMS value of 26 m. At the initial moment of time t0=0 s, the receiver is situated at the zero meridian (zero longitude), at the equator, at a height of 1000 m, and it is moving along the Y-axis with the constant speed of 10 m/s.
As can be seen from FIGS. 3-5, a change in the number of observed satellites causes a jump (discontinuous increase) in the RMS error of the snapshot coordinate estimates.
In the differential positioning mode, the roving receiver position is determined relative to a reference receiver. In this case, the impact of the correlated errors decreases dramatically. These correlated errors are:
Errors in the transmitted Ephemeris data;
Errors in the transmitted clock, including Selective Availability;
Ionospheric refraction; and
Tropospheric refraction.
Nevertheless, it is true for differential positioning too, that the shadowing of some of the observed navigational satellites causes a large discontinuity (a stepwise increase) in the RMS error for coordinate estimates of the roving receiver. FIGS. 6-8 show the root-mean-square (RMS) error of the snapshot differential estimate of coordinates versus time when shadowing of the observed navigational satellites occurs according to the scenario used for FIGS. 3-5. The calculated value of the dilution of precision for the corresponding coordinate in this case is also stepwise increased by an amount that is similar to that indicated in FIGS. 3-5.
The snapshot approach is insensitive to system dynamics, because the solution is based solely upon current measurements, and the solution has no lag during dynamic movements if current measurements are used for each satellite in the solution.
Kalman Filtering
To reduce the impact of large discontinuities in the geometric dilution of precision upon the coordinate estimate errors of the roving receiver, the Kalman method of generating filtered estimates may be used. This method is described in Parkinson, Vol. I pages 409-433, and in Brown, et al., Introduction to random signals and applied Kalman Filtering: with MATLAB exercises and solutions, third edition, John Wiley and Sons, pages 443-445.
The filter has a state vector, which usually comprises the following eight components: the position coordinates (three components), the velocities (three components), as well as the time offset of the receiver and the increment of its time offset with respect to the system time (see Parkinson, Vol. I, page 421.).
On the basis of a priori information about the receiver""s movement (such as provided by kinematic models of the receiver""s movement), the predicted value of the filter""s state vector is formed. The filtered estimate of the state vector is then formed as the linear combination of the predicted value of the state vector and of the current (input) measurement information (the pseudo-range measurements and the Doppler frequency shift). The weight factors are defined on the bases of a priori information on the covariance matrix of the predicted state vector and the measurements error covariance matrix. After correction of the state vector estimate on the bases of the receiver movement models (via the assumed process dynamics) and of the models of measurement errors, the new covariance matrix of the predicted state vector is computed.
Using the Kalman filter method of generating the filtered estimates leads to the significant complication in the processing of the incoming measurement information in comparison with the snapshot-solution method and, as a rule, leads to an increase in the computing expenses in the receiver. For example, for the formation of the snapshot solution coordinate estimates with the LSM it is necessary to execute the operation of inversion of the matrixes of size 4-by-4, but for the formation of the filtered estimates by the Kalman filter method using the eight-dimensional state vector it is necessary to execute inversion of the matrixes of size 8-by-8.
As another drawback, the efficient use of the Kalman filter method requires that the estimated parameters could be presented as random processes generated by a linear system of white Gaussian noise sources, and that the measurement noises are non-correlated. Actually these conditions are never met exactly in the task of determining position coordinates from global-positioning satellite signals. For example, the receiver coordinates are, in reality, bound to the receiver""s acceleration by a set of nonlinear differential equations, and the pseudorange measurement errors listed above are correlated, except for the thermal noises, which are usually not correlated. So real variations of the acceleration, which are poorly described by the movement model used in the filter, bring about the appearance of greater dynamic errors in the receiver coordinate estimates.
For example, when the Kalman filter with an eight-dimensional state vector is used, the acceleration is (in theory) simulated by a white Gaussian noise source. But when in actuality the acceleration has a constant and sufficiently large value over some time interval, greater dynamic errors in the receiver coordinate estimates appear.
FIGS. 9-11 show the RMS errors in the three filtered coordinate estimates versus time when some of the observed navigational satellites are shadowed. During the simulated shadowing event, the number of observed satellites decreases to four. In these simulated results, the receiver is assumed to have no acceleration. The calculated value of dilution of precision for the corresponding coordinate increases stepwise by the value specified in the corresponding FIGS. 9-11. The dilution of precision is in correspondence with designations and symbols used in Parkinson, Vol. I, page 474. For the differential mode measurements, FIGS. 12-14 show the RMS errors of the three filtered coordinate estimates versus time under the same shadowing scenario. In FIGS. 9-14, the RMS errors of the Kalman filter are identified as the xe2x80x9cmeasured rms errorxe2x80x9d.
As can be seen from FIGS. 9-11 and FIGS. 12-14, when Kalman filtering is used to estimate the coordinates, the RMS errors in the estimates varies without steps or sharp jumps, even at the presence of jumps in the dilution of precision. We note that while the decrease at time t300 is relatively fast, it is still smooth and not step-like.
However, acceleration pulses cause larger dynamic errors in the estimates from the Kalman filter than in the estimates from instantaneous snapshot solutions. The dynamic errors in the Kalman estimates are mostly due to the lagging time response of the Kalman filter. The effects of the dynamic errors can be seen in the measured mean error The dynamic errors in the Kalman-filtered coordinates are measured for an exemplary acceleration pulse directed along the Y-axis whose form and parameters are shown in FIG. 15. Using the same simulation scenario described above with respect to FIGS. 3-14, but with the inclusion of the acceleration, the measurement results (RMS and mean errors) are presented in FIGS. 16-18 for the SAN mode and in FIGS. 19-21 for the DGPS mode. In these figures, and in the following FIGS. 22-27, the acceleration pulse specified in FIG. 15 starts at time t195=195 s. The RMS errors from the Kalman filter are identified as xe2x80x9cMeasured RMS errorsxe2x80x9d, and the mean errors (dynamic errors) from the Kalman filter are identified as xe2x80x9cMeasured mean error.xe2x80x9d
Similar results are presented in FIGS. 22-24 and FIGS. 25-27, but for the case when the shadowing of the navigational satellites is absent.
As can be seen from the presented figures, the use of the Kalman filtering at the presence of the receiver acceleration pulse leads to large dynamic errors of the coordinate estimates, as can be seen in the measured mean errors.
To reduce the dynamic errors, it is necessary to reduce the response time (lag effect) of the Kalman filter. However, such a reduction increases the RMS errors in the coordinate estimates. To reduce the dynamic errors caused by acceleration, the model of the receiver""s motion in the Kalman filter may be made more complex to more exactly account for real conditions. However, this significantly complicates the processing of the measurement data.
Using a Kalman filter under differential mode measurements enables one to reduce the influence of large discontinuities (sharp changes) in the geometric factor (GDOP) upon the estimates of the position coordinates. However, in the Kalman filter, there exist large dynamic errors in the coordinate estimates (both under differential and under absolute/stand-alone mode measurements) that are caused by the presence of acceleration pulses in moving receiver.
The McBurney Method
Other method to reduce effects of jumps (large discontinuities) in the dilution of precision upon the value of errors of the receiver coordinate estimates was proposed in U.S. Pat. No. 5,590,043, issued to McBurney. In this patent, filtration is used to reduce large discontinuities in a sequence of the coordinates samples, caused by a number of reasons, among which one is the xe2x80x9c(1) change of the satellites in the SATPS solution constellationxe2x80x9d. This reduction is achieved by forming the filtered coordinate estimates as a linear combination of the coordinate measurements {tilde over (P)}x,n, {tilde over (P)}y,n, {tilde over (P)}z,n, and of a set of predicted coordinate values {circumflex over (P)}xe2x80x2x,n, {circumflex over (P)}xe2x80x2y,n and {circumflex over (P)}xe2x80x2z,n that are computed with the use of the average values of velocities (Vx,n+Vx,nxe2x88x921)/2, (Vy,n+Vy,nxe2x88x921)/2, and (Vz,n+Vz,nxe2x88x921)/2, on the time interval tnxe2x88x921xe2x89xa6txe2x89xa6tn between two time epochs.
The predicted values of the coordinates {circumflex over (P)}xe2x80x2x,n, {circumflex over (P)}xe2x80x2y,n and {circumflex over (P)}xe2x80x2z,n in the specified McBurney patent are computed in correspondence with the expressions:
{circumflex over (P)}xe2x80x2x,n={circumflex over (P)}xcex9x,nxe2x88x921+(Vx,n+Vx,nxe2x88x921)xc2x7xcex94tn/2,xe2x80x83xe2x80x83(1)
{circumflex over (P)}xe2x80x2y,n={circumflex over (P)}xcex9y,nxe2x88x921+(Vy,n+Vy,nxe2x88x921)xc2x7xcex94tn/2,xe2x80x83xe2x80x83(2)
and
{circumflex over (P)}xe2x80x2z,n={circumflex over (P)}xcex9z,nxe2x88x921+(Vz,n+Vz,nxe2x88x921)xc2x7xcex94tn/2,xe2x80x83xe2x80x83(3)
where xcex94tn=tnxe2x88x92tnxe2x88x921 is the duration of the time interval between two epochs;
{circumflex over (P)}xcex9x,nxe2x88x921, {circumflex over (P)}xcex9y,nxe2x88x921 and {circumflex over (P)}xcex9z,nxe2x88x921 are the filtering estimates of the coordinates for the moment tnxe2x88x921.
However, if the receiver velocity varies through the time interval tnxe2x88x921xe2x89xa6txe2x89xa6tn between two epochs, greater dynamic errors arise when the coordinate increments are generated in the forms:
(Vx,n+Vx,nxe2x88x921)xc2x7xcex94tn/2,
(Vy,n+Vy,nxe2x88x921)xc2x7xcex94tn/2,
and
(Vz,n+Vz,nxe2x88x921)xc2x7xcex94tn/2.
The above coordinate increments are used for generating the predicted coordinates {circumflex over (P)}xe2x80x2x,n, {circumflex over (P)}xe2x80x2y,n, {circumflex over (P)}xe2x80x2z,n, and therefore errors in the predicted coordinates will be caused by errors in the coordinate increments.
The errors of coordinate increments were estimated by use of a simulation model.
In FIGS. 28-42, the value of dynamic errors versus time for the above-considered scenario are presented (heavy dots, scale on the right). (The scenario used to generate the results presented in FIGS. 28-42 is similar to the scenario for FIGS. 3-14 with consideration for the fact that the roving receiver is affected by the acceleration pulse.)
The value of the dynamic errors depends upon both the parameters of the acceleration pulse, and the duration of the time interval over which the average velocities Vx,n, Vy,n and Vz,n are determined. FIGS. 28-30 correspond to the case where the aforesaid time interval is equal to the duration of the time interval xcex94tn between two epochs. FIGS. 31-33 correspond to the case, where the aforesaid time interval is equal to a half of the duration of the time interval between two epochs (xcex94tn/2). FIGS. 34-36, FIGS. 37-39 and FIGS. 40-42 show similar dependencies for the time intervals of: xcex94tn/4, xcex94tn/16, and xcex94tn/18, respectively.
As one can see, the dynamic errors in determining the coordinate increments in the considered case can be several tens of meters.
The root mean square errors in the coordinate increments during fixed (non-moving) measurements also vary with the duration of the time interval over which the average velocities are defined. The RMS errors are shown by light dots in the figures, with the corresponding scale on the left side of the figure.
In the McBurney method, large dynamic errors due to acceleration of receiver appear under differential and absolute measurement modes. FIGS. 43-48 show the mean errors in the Y-coordinate (which best show the dynamic errors because the acceleration pulse is in the Y-direction) versus time for the above scenario. The mean error is shown with heavy dots in each figure, with the scale on the right side of the figure. The root mean square error is shown with light dots in each figure, with the scale on the left side of the figure. The figures use different time intervals for the computation of the average velocities Vx,n, Vy,n and Vz,n. For FIGS. 43-48, these intervals are, respectively, xcex94tn, xcex94tn/2, xcex94tn/4, xcex94tn/6, xcex94tn/8, and xcex94tn/12.
The root mean square errors of the estimate of the receiver""s velocity under differential measurements are varied when changing the duration of the time interval on which the average velocities Vx,n, Vy,n and Vz,n are defined. In turn, these variations result in changing the RMS error estimates of the receiver""s coordinates. The measured values of mean square error are presented in the same FIGS. 43-48 by dots (light dots, with the scale on the left).
The accuracy of estimates of the moving receiver coordinates, both absolute and differential, may be improved by the methods and apparatuses of the present invention.
The present invention encompasses methods and apparatuses for generating the estimates of a receiver""s coordinates ({circumflex over (P)}fx,n, {circumflex over (P)}fy,n, {circumflex over (P)}fz,n) and/or time offset ({circumflex over (P)}fxcfx84,n) for a moment of time tn without large errors caused by short-term shading of a part of the observable global positioning satellites and also without large dynamic errors caused by the receiver movement The receiver may be stationary or mobile (i.e., rovering). Each satellite signal is transmitted by a corresponding satellite, and enables the receiver to measure a pseudorange between itself and the corresponding satellite.
A preferred general embodiment of the present invention comprises, after an initial set up of parameters at the initial time moment n=0, the reiteration of the following steps for each subsequent time moment n greater than 0:
(a) Obtaining a set of snapshot-solution values ({tilde over (P)}x,n, {tilde over (P)}y,n, {tilde over (P)}z,n, {tilde over (P)}xcfx84,n) for the position coordinates and time offset of the receiver at the time moment tn. These values may be obtained by generating the snapshot-solution values directly, or by receiving them from another process which generates these values.
(b) Generating a set of predicted position coordinates and time offset ({circumflex over (P)}xe2x80x2x,n, {circumflex over (P)}xe2x80x2y,n, {circumflex over (P)}xe2x80x2z,n, and {circumflex over (P)}xe2x80x2xcfx84,n) for the time moment tn from a measurement of a plurality of satellite carrier phases during a time interval preceding time moment tn and from a set of values for the position coordinates and time offset of the receiver at a previous time moment tnxe2x88x921. In preferred implementations, the set of values at the previous time moment can be provided by steps (a) or (e) (see below) for time moments n greater than 0, and by an initialization process for the initial time n=0.
(c) Generating a first quality factor Qn which is representative of the accuracy of the set of snapshot solution values.
(d) Generating a second quality factor Qnxe2x80x2 which is representative of the accuracy of the set of predicted position coordinates and time offset. And
(e) Generating a set of refined estimates ({circumflex over (P)}fx,n, {circumflex over (P)}fy,n, {circumflex over (P)}fz,n, {circumflex over (P)}fxcfx84,n) for the position and time offset of the receiver based on the quality factors, the snapshot solution values, and the predicted position values.
It may be appreciated that above is a preferred general embodiment, and that the present invention, as described and claimed herein, fully encompasses the cases where only one, two, or three of the four estimates ({circumflex over (P)}fx,n, {circumflex over (P)}fy,n, {circumflex over (P)}fz,n, {circumflex over (P)}fxcfx84,n) is generated. In such embodiments, correspondingly fewer components of the snap-shot and predicted values need to be obtained or generated. Also, it should be understood that the claims, in their broadest interpretation, apply to the cases where steps (a)-(e) are performed once, to cases where steps (a)-(e) are consecutively reiterated over a plurality of time moments, and to cases where steps (a)-(e) are performed at selected time moments with other processing may be applied during the other time moments.
In one group of preferred embodiments, the set of refined estimates ({circumflex over (P)}fx,n, {circumflex over (P)}fy,n, {circumflex over (P)}fz,n, {circumflex over (P)}fxcfx84,n) is generated as a first multiplier (xcex1n) of the set of snapshot-solution values plus a second multiplier (1xe2x88x92xcex1n) of the set of predicted values, with the sum of the first and second multipliers being equal to 1, and preferably with both multipliers being less than or equal to 1. The first multiplier (xcex1n) is greater than the second multiplier (1xe2x88x92xcex1n) when the first and second quality factors indicate that the set of snapshot-solution values is more accurate than the set of predicted values, and the second multiplier (1xe2x88x92xcex1n) is greater than the first multiplier (xcex1n) when the first and second quality factors indicate that the set of predicted values is more accurate than the set of snapshot-solution values. Further preferred embodiments provide for preferred methods of generating the first and second multipliers.
In another group of preferred embodiments, the set of refined estimates ({circumflex over (P)}fx,n, {circumflex over (P)}fy,n, {circumflex over (P)}fz,n, {circumflex over (P)}fxcfx84,n) is generated as the set of snapshot-solution values when the first and second quality factors indicate that the set of snapshot-solution values are more accurate than the set of predicted values, and as the set of predicted values when the first and second quality factors indicate that the set of predicted values is more accurate than the set of snapshot-solution values.
A number of preferred methods of generating the first and second quality factors are disclosed herein, and may be used with any of the above described methods.
The methods outlined above provide for highly accurate estimates for the receiver""s position and time offset (and therefore time scale) without the previously-described detrimental effects caused by the shadowing of satellites or the movements of the receiver. While the present invention provides refined estimates for the receiver""s position and time offset, it may be appreciated that practitioners in the art may wish to use the present invention to generate refined estimates for only the receiver""s position, or for only the receiver""s time offset, rather than for both the receiver""s position and time offset. Practitioners may also wish to use the present invention to generate estimate for only two of the three position coordinates (such as when one is already known), or for only one position coordinate (such as when two coordinates are already known).
Accordingly, it is an objective of the present invention to provide for refined estimates of the position and/or time offset (time scale) of a receiver which are more accurate during short-term occurrences of shadowing of satellites and which do not have errors which jump in response to start of an occurrence of shadowing.
It is another objective of the present invention to provide for refined estimates of the position and/or time offset (time scale) of a receiver which maintain their accuracy during movement of the receiver, and particularly during acceleration of the receiver.
These and other objectives of the present invention will be apparent from the detailed description of the present invention.